Working paper title: Tax progressivity and income inequality: A simple formula 

By: Julius Andersson

Abstract

This paper shows that the Kakwani index of tax progressivity for indirect taxes can be approximated by K=(eta - 1) G, where 'eta' is the income elasticity for the taxed good and G is the Gini coefficient. It follows that when the elasticity differs from unity, income inequality amplifies the magnitude of tax progressivity. A tax on necessities becomes more regressive as inequality rises; a tax on luxuries more progressive. If elasticities vary across the income distribution, this amplification is compounded. Tax progressivity thus depends on two sufficient statistics, yielding a simple formula for evaluating carbon, excise, and other indirect taxes.